%I #5 Jul 21 2018 10:05:37
%S 1,1,1,2,2,4,4,6,7,10,11,16,17,23,27,34,38,50,54,70,79,97,107,135,148,
%T 180,205,243,270,328,360,429,480,561,625,738,810,949,1057,1219,1349,
%U 1571,1723,1986,2206,2515,2776,3188,3496,3983,4408,4980,5485,6228,6826
%N Number of integer partitions of n whose multiplicities are weakly increasing and span an initial interval of positive integers.
%e The a(7) = 6 integer partitions are (7), (61), (52), (43), (421), (331).
%t normalQ[m_]:=Union[m]==Range[Max[m]];
%t Table[Length[Select[IntegerPartitions[n],And[normalQ[Length/@Split[#]],OrderedQ[Reverse[Length/@Split[#]]]]&]],{n,60}]
%Y Cf. A000041, A000837, A055932, A242031, A317081, A317082, A317085, A317087, A317090.
%K nonn
%O 0,4
%A _Gus Wiseman_, Jul 21 2018